RAI, the state television broadcaster, aired a video of the incident, showing the escalator suddenly accelerating, with people piling up at the bottom.
An accident involving an escalator in the Rome metropolitan system has injured about 20 people, mostly Russian soccer fans.
Separately, one CSKA fan was slashed with a knife during clashes between opposing fans outside the Stadio Olimpico, the ANSA news agency reported.
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People on the parallel escalator can be seen trying to grab those on the broken machine and pull them to safety.
Emergency services are at the scene and the station has been closed, Italian news agency Ansa reported.
There were also reports of one Russian visitor being stabbed with a knife, but they were later refuted by the Italian embassy in Moscow.
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Most who were injured were reportedly fans of the visiting Russian soccer team CSKA Moscow, who were in town for an evening Champions League match against Rome's team.
Witnesses quoted by police said the Russian fans had been singing and jumping before the escalator gave way.
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They are two legends and when they are playing like this, it sometimes feels like they are playing PS4", said the leg-spinner. Whenever he gets there, Kohli will be the fastest to do so and again beat Tendulkar to the record.